We test the hypothesis that metal-poor globular clusters form within disk galaxies at redshifts z>3. We calculate the orbits of model clusters in the time-variable gravitational potential of a Milky Way-sized galaxy, using the outputs of a cosmological N-body simulation. We find that at present the orbits are isotropic in the inner 50kpc of the Galaxy and preferentially radial at larger distances. All clusters located outside 10kpc from the center formed in satellite galaxies, some of which are now tidally disrupted and some of which survive as dwarf galaxies. Mergers of the progenitors lead to a spheroidal spatial distribution of model clusters, although it is more extended than that of Galactic metal-poor clusters and has a somewhat shallower power-law slope of the number density profile, {gamma}~2.7. The combination of two-body relaxation, tidal shocks, and stellar evolution drives the evolution of the cluster mass function from an initial power law to a peaked distribution, in agreement with observations. However, not all initial conditions and not all evolution scenarios are consistent with the observed mass function of the Galactic globular clusters. We find that our best-fitting models require the average cluster density, M/R^3^h, to be constant initially for clusters of all mass and to remain constant with time. However, these models do not explain the observed decrease of the mean density with galactocentric distance. Both synchronous formation of all clusters at a single epoch (z=4) and continuous formation over a span of 1.6Gyr (between z=9 and 3) are consistent with the data. For both formation scenarios, we provide online catalogs of the main physical properties of model clusters.